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40th Annual Symposium on Foundations of Computer Science
Cuts, Trees and -Embeddings of Graphs
New York, New York
October 17-October 18
ISBN: 0-7695-0409-4
Anupam Gupta, University of California at Berkeley
Alistair Sinclair, University of California at Berkeley
Ilan Newman, University of Haifa
Yuri Rabinovich, University of Haifa
Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into \math space. The main results are: 1. Explicit constant-distortion embeddings of all series-parallel graphs, and all graphs with bounded Euler number. These are thus the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, we obtain algorithms to approximate the sparsest cut in such graphs to within a constant factor. 2. A constant-distortion embedding of outerplanar graphs into the restricted class of \math-metrics known as "dominating tree metrics". We also show a lower bound of \math on the distortion for embeddings of series-parallel graphs into (distributions over) dominating tree metrics. This shows, surprisingly, that such metrics approximate distances very poorly even for families of graphs with low treewidth, and excludes the possibility of using them to explore the finer structure of \math-embeddability.
Index Terms:
Multicommodity flow, Sparsest cut, <IMG height=18 alt="" src="EQN76.GIF" width=13 border=0> embeddings, Finite metric spaces
Anupam Gupta, Alistair Sinclair, Ilan Newman, Yuri Rabinovich, "Cuts, Trees and -Embeddings of Graphs," focs, pp.399, 40th Annual Symposium on Foundations of Computer Science, 1999
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